Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) = x₁ using the following values. A = x(t) = 5-6 40 [; -2]·--[*]-[:] f(t) = 60 0 x(0) = eAt 0 1-et+6e4t 6e-t-6e4 -e-t+e4t 6e-t-e4t 4t

Q: -5x2 – 3 If f(x) = then f'(0) is 4х + 2 O - 3 О 13 O - 1/3 Оз

A: Solving the problem by obtaining the derivative.

Q: 3. (a) Which of the following functions have 5 in their domain? f(x) = x² - 3x *- 5 h(x) = Vx - 10…

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Q: x-²²-3 ²-3, determine the x-value(s) where f(x) changes from concave up to concave down. f(x)= Ox=…

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Q: Find a formula for f-(x) and (f-1)'(æ) if ƒ(x) = -V5 – x f-' (x) = (5-1)'(x) =

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Q: If the function f(x) is defined as f(x) = = (4-2√√x)² √x -,x>0 Then, what is the value of ƒ'(16) = ?

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Q: If ƒ(x) = 3x√x + ƒ'(9) = x²√x then ←

A: f(x)=3xx+2x2xwe know  ax×ay=ax+yd dx(xn)nxn-1

Q: if f(x)={ -3x       for x -1  find f(-2)  a. -6 b.9 c.6  d.-1 e.0

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Q: If 87 + 2 f(x) + 3x² (ƒ(x))³ = 0 and ƒ(1) = −3, find ƒ'(1).

A: 87+2f(x)+3x2(f(x))3=0,f(1)=−3

Q: Given f (x) find f^−1 (x) for each of the following:  f (x) = 2x−3/7+x

A: Given function is:

Q: Find the linear approximation of f(x)=√x when x = 81. 1 108 O L(x)=3+ -(x-81) OL(x)=81+ 1 108…

A: We have given function  fx=x4 Put x=81 f81=814=344=3 Linear approximation at x=a is given as…

Q: If f(x) = √2x + 7, find f'(x). Find f'(1).

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find the max or min value of /x) -3x + 6x + 4

A: We have to find the maximum or the minimum value of the following function -  f(x) = -3x2+6x+4

Q: 1)y = (8 + 7x³) 2)y = (x + 5)(2x+3) Find the derivative of the following functions (answer only two)…

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Q: f (x) = 3r³ – 9x² 1 + x +3 j(x) = x + 7x + 9 Determine p'(x) given p(x) = f(x)j(x). Please don't…

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Q: Sketch the following functions. Show all your work. N a) Domain b) Intercepts c) Symmetry d)…

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Q: Let f(x) = -2x√√x + f'(x) = -8 x²√x

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Q: Find h(x) if h'(x)= h(x): 5x (6-x²)² X and h(1) = -6.

A: NOTE: Refresh your page if you can't see any equations. . here we have take integration on both…

Q: Find the derivate of the function: a) f(x) = x²(x²-8) F'(x) = 2 b) f(x) = (5x²³-7) (6x + 1) = 3 c)…

A: Since you have posted multiple question in this question so i have solved the first three subpart…

Q: Suppose f(5) - 9 and f'(5) = = - 3. - An object moves along the curve y³ - 3x² f(x) = 5x = 649. For…

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Q: Consider the following. f(x)=x²-6x² + 7

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Q: 10. If f(x) = 2x³ - 3 x3, then f'(1) is which of the following? (B) -3 (C) -15 (E) 7 (A) 15 (D) -1

A: given function is

Q: 2. Find the x-intercepts for g(x)= 3x² -12x² - 36x

A: To find the x intercept we have to put y = g(x) =0

Q: If f(x) = f'(x) = f'(1) = 6x + 2 7x + 2 find: 2 (7x + 2)² 28 (7x+2)³ X

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Q: 5x +2 Q5. If f(x)=: 3x -x then find f'(2)

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Q: 10) Find (¹) (3) if f(x)=x²+x-1.

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Q: If 46 +3ƒ(x) + 5x²(ƒ(x))³ = 0 and ƒ(−1) = −2, find ƒ'(-1). f'(-1) = 0

A: Given46+3f(x)+5x2f(x)3=0f-1=-2   We are required to findf'(-1)